Effects of a locally injected signal on phase synchronization in a network of self-excited cells

We consider in this paper the problem of phase synchronization in a network of coupled self-excited cells with free-end boundary conditions. The eigenvalues properties are used to perform the stability boundaries of the synchronization process for pure sinusoidal and quasi-sinusoidal oscillatory states. In the case where the cells’ oscillatory states are quasi-periodic, more energy and time are required for the network to become fully synchronized, compared to the case where each cell exhibits a periodic oscillation. The influence on the stability boundaries of a periodic external excitation locally injected in the network is tackled. For both cases (with and without local injection), numerical simulations are used to check the accuracy and to complement the results derived from the analytical treatment. In this configuration, the local injection helps to drastically increase the range of the coupling parameter for which all cells become synchronized.